Dry the tomatoes: Rinse the cherry tomatoes and pat them dry with paper towels until no moisture beads remain on the skin.
Dry the mozzarella: Drain the mozzarella balls from their liquid and blot them dry with paper towels so the olive oil clings to the surface later instead of sliding off.
Wash the basil: Rinse the basil leaves gently under cool water and lay them on a towel until fully dry, about 5 minutes.
Fold the basil leaf: Take one basil leaf per skewer and fold it in half so it curves around the tomato instead of lying flat.
Thread the skewer: Push a cherry tomato onto the skewer first, followed by the folded basil leaf, then a mozzarella ball, sliding each piece down gently so nothing splits.
Repeat for all skewers: Continue threading the remaining tomatoes, basil, and mozzarella in batches of about 10 at a time until all 20 skewers are done.
Arrange on a platter: Lay the finished skewers in neat rows or a circular pattern on a serving platter, leaving a little space between each one.
Drizzle with olive oil: Pour the olive oil over the skewers in a thin, even stream so each one gets a light coating.
Add the balsamic glaze: Zigzag the balsamic glaze across the platter until it pools lightly in the gaps between the tomatoes and mozzarella.
Season and serve: Sprinkle flaky sea salt and cracked black pepper over the top right before serving so the salt stays crisp and visible.